Benchmarking conditioners in Liang–Kleeman Information Flow: application to land–atmosphere interactions in humid forests

Siddique, Fareeha; Hagan, Daniel Fiifi Tawia; Wang, Guojie; Docquier, David; Vannitsem, Stéphane

doi:10.5194/esd-17-1551-2026

Articles | Volume 17, issue 5

https://doi.org/10.5194/esd-17-1551-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/esd-17-1551-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 17, issue 5

Research article

|

20 Oct 2026

Research article |

| 20 Oct 2026

Benchmarking conditioners in Liang–Kleeman Information Flow: application to land–atmosphere interactions in humid forests

Fareeha Siddique, Daniel Fiifi Tawia Hagan, Guojie Wang, David Docquier, and Stéphane Vannitsem

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Final revised paper (published on 20 Oct 2026)
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Preprint (discussion started on 26 Jan 2026)
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Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2026-267', Anonymous Referee #1, 27 Mar 2026
This paper investigates when and why bivariate and multivariate Liang–Kleeman Information Flow (L-K IF) estimates diverge in land–atmosphere applications. The manuscript has clear potential and addresses an interesting methodological problem of practical relevance. However, substantial revisions are required to strengthen the manuscript.
Reviewer's comments:
The paper defines ΔIF as an absolute difference in Section 2.2, but Appendix A later writes ΔIF expressions without absolute value signs.

The significance assessment of ΔIF via a paired two-tailed Student’s t-test at each time step is not sufficiently justified. Because the IF estimates are time-varying, serially dependent, and derived from filtered time series, the independence assumptions behind a pointwise t-test may not hold.

The choice of four quantile-based regimes is reasonable but somewhat arbitrary. The manuscript should explain why quartiles were selected instead of terciles, quintiles, or physically defined thresholds. A short sensitivity test would be helpful.

According to the authors, the definition of CR depends on a threshold ε_abs chosen as, for example, the 10th percentile of ΔIF across all couplings. This choice strongly affects CR yet is not sufficiently justified or stress-tested. Sensitivity analysis is needed because CR may change substantially under alternative thresholds.

The paper should report the employed Kalman filter parameter settings.

ANOVA is interesting, but readers need reassurance that its assumptions are not severely violated under quantile-conditioned, potentially heteroscedastic, non-independent data. A discussion on robustness is required.

The new indices (MDI, MG, CP, and CR) are interesting, but they currently read more as descriptive summary statistics than as fully validated methodological advances. Their novelty would be stronger if the authors demonstrated formal properties, sensitivity (do results change if noise increases? time series length changes? conditioning set slightly changes?), robustness, and interpretability (What does a high MDI physically mean?) across more than one showcased pathway.

The decomposition in Eqs. (7)–(9) is order-dependent, since conditioners are added progressively. The manuscript does not discuss whether MDI, MG, and CP change if the order of VPD, T, and SSR is permuted. This is a major issue because the estimated “contribution” of each conditioner may partly reflect the order rather than intrinsic causal relevance. The authors should test all permutations.

Careful language editing is required throughout the manuscript. Examples include awkward phrasing such as “This begs a spatio–temporal quality…,” “more direct SM→LAI,” “VPD_driver-based,”.
Citation: https://doi.org/10.5194/egusphere-2026-267-RC1
- AC1: 'Reply on RC1', Daniel Hagan, 30 Apr 2026
  
  Dear Referee #1,
  We thank you for your detailed and constructive comments. Please find attached our point-by-point response.
  
  Citation: https://doi.org/10.5194/egusphere-2026-267-AC1
RC2:
'Comment on egusphere-2026-267', Anonymous Referee #2, 10 Apr 2026

Please see the attached PDF with the reviewer comments.

Citation: https://doi.org/10.5194/egusphere-2026-267-RC2
- AC2: 'Reply on RC2', Daniel Hagan, 30 Apr 2026
  
  Dear Referee #2,
  We thank you for your detailed and constructive comments. Please find attached our point-by-point response.
  
  Citation: https://doi.org/10.5194/egusphere-2026-267-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Reconsider after major revisions (17 May 2026) by Kira Rehfeld

AR by Daniel Hagan on behalf of the Authors (18 May 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (02 Jun 2026) by Kira Rehfeld

RR by Anonymous Referee #3 (28 Jun 2026)

Suggestions for revision or reasons for rejection

This manuscript applies the multivariate, time-varying LKIF framework to compare bivariate and multivariate information-flow estimates via ΔIF and related diagnostics (MDI, MG, CP, CR), focusing on SM/VPD → LAI/GPP couplings in Southeast China and the Amazon Basin. The topic is relevant and the paper is generally readable. The revision adds useful material on Kalman settings, CR thresholds, quantile sensitivity, conditioner-order permutations, and an expanded Discussion.
However, when the original manuscript is read together with the point-by-point response, several fundamental issues remain inadequately addressed. Responses often rely on wording changes, supplementary sensitivity plots, or deferral to future work, rather than targeted analyses. Although Liang–Kleeman information flow (LKIF) is now used widely across atmospheric, oceanic, financial, and other applications, the central claim of this paper—that the bivariate–multivariate IF difference can characterize whether a physically meaningful mechanism is present between driver and response—is not yet sufficiently supported in terms of causal identification and synthetic validation. Major revision is required before the main conclusions can be considered robust:
1. Title overstates scope; representativeness concern not substantively answered
The title “Benchmarking Conditioners in Liang–Kleeman Information Flow” suggests a systematic benchmark, yet the study is a limited application to two small humid-forest domains and a handful of variables/pathways. There is no comprehensive or global analysis, and Appendix A does not constitute a conditioner benchmark in the strict sense. It is recommended that using a more modest title (e.g., … A Case Study of Land–Atmosphere Interactions in Humid Forests, or … A Simple Application to Land–Atmosphere Interactions); tone down global claims; state explicitly that real-data inferences are restricted to humid forests.
Besides, reviewer 2 raised this explicitly (Major Comment 5). In review.pdf, the authors mainly reworded the Abstract/Conclusions and flagged broader biomes as future work. No additional regions or biome contrasts were added. The revised Abstract sentence—“even for the same variables … differently at different locations”—emphasizes spatial heterogeneity but does not answer whether conclusions from two humid forests generalize elsewhere. This reads as deflecting the representativeness criticism rather than addressing it.
2. For Southeast China SM→GPP (Fig. 1c), bivariate IF is mostly insignificant except around 2011, whereas SM→GPP|VPD,T,SSR is significant in multiple periods. Conditioning therefore changes both magnitude and significance. Appendix A instead emphasizes directional fidelity and near-zero false links, with bivariate and multivariate curves nearly overlapping for x₁→x₂. It does not reproduce significance transitions or large conditioning effects. This is not a strict logical contradiction, but a major evidential gap: synthetic validation does not support the paper’s central real-data message.
3. Appendix A does not systematically test chain, observable fork, collider, direct+indirect, or joint multivariate conditioning as in the main text.
For example, if X₅ is observed but X₄ is an unobserved mediator on X₂→X₄→X₅, can LKIF in subsystem (X₁,X₂,X₃,X₅) avoid misattributing X₄’s role? If X₁→X₂→X₄ and X₁→X₃→X₄ contribute with opposite signs and similar magnitudes, bivariate T(X₁→X₄) may cancel, and T(X₁→X₄|X₂,X₃) may remain similarly small. Then |ΔIF| is small and CR is high even though X₂ and X₃ are essential—contradicting the claim that small |ΔIF| implies bivariate sufficiency.
4. Land–atmosphere memory often spans weeks to months. The study uses monthly anomalies and contemporaneous LKIF via Kalman covariances, with no explicit lag structure.
5. Fig. 2: High/low ΔIF periods are illustrated with one year each for causal graphs, without demonstrating representativeness or a formal selection algorithm beyond post-hoc labeling. Why not composite graphs from all high-|ΔIF| or low-|ΔIF| years? Single years may reflect outliers, extremes, or estimator artifacts rather than typical architecture.
6. Mapping +IF/−IF to vulnerability/resilience is not part of the strict LKIF definition. If intended as an ecological extension, it requires independent justification and citations; otherwise it belongs in Discussion as heuristic interpretation—or a separate paper.
7. Fig 3: In cells such as SM(Q1)–VPD(Q1), |r_IF| appears blank/white while |ΔIF| is non-zero. The caption explains cross-hatching for “no data” but not why correlation is unavailable while |ΔIF| is shown (likely small n, zero variance, or inconsistent computation rules). This undermines Section 3.3.
8. Because it is impossible in practice to include the full Earth-system state vector in LKIF computation, and because currently implementable IF algorithms—whatever the generality of the underlying theory—operate under linear approximations in applied settings, the authors should use numerical simulation more systematically to validate the causal pathways inferred from observations. Without such validation, it is difficult to distinguish physically meaningful conditioning effects from artifacts of omission, linearization, or sparse sampling.

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RR by Anonymous Referee #4 (02 Jul 2026)

Suggestions for revision or reasons for rejection

Review of manuscript MS No.: egusphere-2026-267
Title: Benchmarking Conditioners in Liang–Kleeman Information Flow: Application to Land–Atmosphere Interactions
Author(s): Fareeha Siddique, Daniel Fiifi Tawia Hagan, Guojie Wang, David Docquier, and Stéphane Vannitsem

The authors present an interesting study of temporal evolution of the Liang–Kleeman Information Flow (LKIF)
in its bivariate and multivariate forms in land–atmosphere interactions. I was asked for an opinion
after the first revision of the manuscript and found that the first two reviews motivated the authors
to make a great improvement of the manuscript. I think, however, that there are still some questions to be answered.

1. The application of the Kalman filter allows for computation of the time-resolved LKIF. Later the authors discuss
how the LKIF and its differences depend on values of involved variables, using combinations of their quartiles.
Considering the LKIF is computed from co/variances, it would be useful to plot means and especially variances
of the involved variables in the same time-resolution as LKIFs in order to see whether the time-evolution of
LKIFs can or cannot be explained by the changes in variances.

2. Typically, the causality measures decrease after conditioning (bivariate - multivariate > 0)
as we can see also in the presented numerical example A3, while in some real data cases in Fig. 1
it is reversed, e.g., SM->LAI < SM->LAI|VPD. How this can be explained?

3. Usually in causality analysis both directions are analysed, here only the causal directions
from meteo/hydro to bio- variables are presented. Was this an intension? The only exception
are the causal graphs in Fig 2, where also arrows e.g. from LAI to T can be seen.
Were the latter obtained from five-variate estimates?

4. In the discussion, Granger causality is characterized as "GC infers lagged directional dependence."
Then LKIF seems like a lag-free measure. However, LKIF uses the derivative of the effect variable, computed
as differenced time series. Here the monthly data are used, so one month is the effective time lag
for which the causal relations are presented. Would different time lags change the results?
(Larger or smaller, the data were subsampled. BTW. the way of subsampling can affect the causality results.)

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RR by Anonymous Referee #5 (11 Jul 2026)

ED: Reconsider after major revisions (22 Jul 2026) by Kira Rehfeld

AR by Daniel Hagan on behalf of the Authors (25 Aug 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (28 Aug 2026) by Kira Rehfeld

RR by Anonymous Referee #4 (08 Sep 2026)

RR by Anonymous Referee #3 (09 Sep 2026)

Suggestions for revision or reasons for rejection

This manuscript applies the multivariate, time-varying LKIF framework to compare bivariate and multivariate information-flow estimates via ΔIF and related diagnostics, focusing on SM/VPD → LAI/GPP couplings in Southeast China and the Amazon Basin. The topic remains relevant and the paper is generally readable. Relative to the previous round, the authors have now provided acceptable responses to most of the comments raised earlier. However, one central issue remains unresolved, and it concerns not a peripheral sensitivity test but one of the paper’s most important empirical findings. For Southeast China SM→GPP (Fig. 1c), the bivariate IF is mostly insignificant except around 2011, whereas the conditioned estimate SM→GPP|VPD,T,SSR is significant over multiple periods. Conditioning therefore changes both magnitude and significance. This is precisely the kind of confounding-/conditioner-related behaviour that the manuscript claims to diagnose. Yet the revision still does not provide a clear account of why this happens—neither from the observational causal analysis itself, nor from an idealized dynamical model, nor from a physically grounded mechanistic interpretation. Without such an account, the credibility of the main conclusion is substantially weakened. Major revision is still required on this point.

Comments on title/scope wording, Appendix A’s limited structural coverage, lag memory, Fig. 2 year selection, IF-sign interpretation, and Fig. 3 missing |rIF| cells have been answered at an acceptable level for this round (through clarification, limitation statements, and/or textual correction). I do not request further major work on those items beyond ordinary consistency checks.

However, previous Major Comments 2–3 noted that Appendix A emphasizes directional fidelity and near-overlapping bivariate/multivariate curves for x_1→x_2 and therefore does not support the Fig. 1c pattern. In the response, the authors agree that Appendix A does not reproduce conditioning-induced significance transitions and add limiting text. That is acknowledgement, not explanation.

What is still missing is a coherent treatment of this finding itself: (i) a focused observational diagnosis of why SM→GPP is weak/insignificant in the bivariate form but significant after conditioning on VPD, T, and SSR—Section 3.1 still speaks of “little adjustments” for SM-driven GPP couplings, which is inconsistent with Fig. 1c and the later diagnostics; (ii) a controlled dynamical example in which a strong direct pathway is masked bivariate and recovered under multivariate conditioning (referring to a different synthetic pathway with only modest amplitude change does not address Fig. 1c); and (iii) a clear land–atmosphere mechanistic interpretation of why the SM→GPP signal should be suppressed in the bivariate projection and revealed after conditioning on atmospheric demand/energy variables. Absent such an account, the result risks being read as an estimator or significance-threshold artefact rather than a physically meaningful confounding/conditioning effect.

Because this pattern is one of the manuscript’s most consequential empirical claims, leaving it unexplained greatly reduces the paper’s credibility. A satisfactory revision must therefore provide a clear exposition along at least one of the three lines above (data diagnosis, idealized model, and mechanistic interpretation), and must correct the inconsistent wording in Section 3.1.

Finally, the Conclusion still states too strongly that when driver–response relationships are “predominantly more direct, conditioners contribute little”. This overreaches relative to the revised Methods/Discussion, which now acknowledge that small |ΔIF| does not establish causal sufficiency, and relative to Fig. 1c, whose bivariate-insignificant / multivariate-significant pattern remains unexplained. The concluding claim should be toned down accordingly.

Minor comments / language
Please also harmonize abbreviations between the main text and figure captions: GPP is expanded inconsistently as “Gross Primary Productivity” and “Gross Primary Production”, while and SSR is inconsistently as “Solar Surface Radiation” and “Surface Solar Radiation”.

L93: and more importantly, the physical limitations leading to their differences.
→
and more importantly, did not clarify the physical limitations leading to their differences.

L316: Fig 1a → Fig. 1a
L322: SM_driven → SM-driven
L326: results in little adjustments → results in few adjustments
L363: southeast China →Southeast China
L420: “Fig. b-d” → “Fig. 3 b–d”
L424: “SM-based couplings (a-c) … VPD-based couplings (b-d)” → “SM-based couplings (a, c) … VPD-based couplings (b, d)”

There are also multiple subject–verb agreement and article/count-noun issues throughout; the following are only examples, and similar problems occur elsewhere in the text: L355: “how these increases or decrease T”→“how these increase or decrease T”; L547: “attempts to understand how conditioners may influence its causal structures is still limited” → “are still limited”

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ED: Reconsider after major revisions (10 Sep 2026) by Kira Rehfeld

AR by Daniel Hagan on behalf of the Authors (14 Sep 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (05 Oct 2026) by Kira Rehfeld

AR by Daniel Hagan on behalf of the Authors (10 Oct 2026)

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Short summary

Understanding causality in Earth-system processes is challenging because multiple drivers act simultaneously and can distort causal estimates. We develop a diagnostic framework using controlled experiments and real land–atmosphere data to identify when external drivers affect how one variable influences another (via Liang–Kleeman Information Flow). This influence depends on system stress, guiding when multivariate conditioning is necessary.